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The costs of congestion in the U.S. air transportation system are substantial, with a recent study estimating these costs at over $30 billion for domestic operations in 2007. We develop a prioritized rationing scheme, Ration by Prioritized Schedule, and show that significant benefits can be achieved through prioritization, even in the face of airline recovery responses. Subsequently, we develop a strategic prioritization game, a non-monetary, market-based scheme for allocating flight priorities which allows airlines to trade-off priorities across airports. In addition to having nice equilibrium properties, we show that our bidding and allocation scheme is capable of achieving some of the benefits of congestion pricing, which has been widely studied in the literature but has met with significant resistance in practice.